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%I #6 Jun 10 2015 05:21:08
%S 57,5767,6497,7387,29177,30967,35657,37627,52891,53297,61937,70747,
%T 75067,96091,114857,118961,126727,145097,190087,194417,215287,221777,
%U 244961,307961,335177,348091,370817,408257,414727,423737,462391,585161
%N Numbers n with the property that the difference between the two largest proper divisors of n equals the sum of proper divisors of the digit sum of n.
%C All but two members of the sequence below 20000000 are the products of two primes separated by 6 or 16 and have digit sums of 25 or 26, which have proper divisor sums of 6 (=1+5) and 16(=1+2+13) respectively. The exceptions are the 1st term (57), which has a digit sum of 12 and the 67th (18999857), which has a digit sum of 56.
%e The divisors of 57 are 1, 3 and 19, so the difference of the two largest is 16.
%e The divisors of its digit sum (12=5+7) are 1,2,3,4 and 6, which also sum to 16.
%t ok[n_] := Block[{d = Divisors@n, s = Total@ IntegerDigits@ n}, Length[d] > 2 && d[[-2]] - d[[-3]] == DivisorSigma[1, s] - s]; Select[Range[10^5], ok] (* _Giovanni Resta_, Jun 09 2015 *)
%o A program to test an individual integer, written in APL, is available if required.
%K nonn,base
%O 1,1
%A Paul H. Smith (decisionbydesign(AT)aol.com), Nov 17 2007
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